Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
نویسندگان
چکیده
منابع مشابه
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the `-Tate pairing in terms of the action of the Frobenius on the `-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the `-Tate pairing restrained to subgroups of the `-torsion which are maximal isotropic with respect to the Weil pairing. First, we ded...
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Let C be a curve of genus 2 and ψ1 : C −→ E1 a map of degree n, from C to an elliptic curve E1, both curves defined over C. This map induces a degree n map φ1 : P 1 −→ P 1 which we call a Frey-Kani covering. We determine all possible ramifications for φ1. If ψ1 : C −→ E1 is maximal then there exists a maximal map ψ2 : C −→ E2, of degree n, to some elliptic curve E2 such that there is an isogeny...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.04.023